Jump to content
Objectivism Online Forum

quantitative "threshold"

Rate this topic


Vik

Recommended Posts

I've used an idea of a quantitative "threshold" to understand some conclusions from the sciences.

case 1: phases of matter.  Consider water expanding before it boils. Water within a sufficiently long tube will expand as you raise the temperature.  There is a proportional relationship between liquid volume of water and temperature throughout a range of temperatures and pressures. But that relationship will not hold above or below certain temperatures and pressures.  There is a quantitative "threshold" between ordinary liquid and ordinary vapour.  What lies beyond the quantitative "threshold" must be explained by a different concept. For example, there are several phases of water, some of which have surprising properties.  It would make absolutely no sense to try to apply proportional expansion of liquid water to water vapour.

case 2: electromagnetic spectrum. We united a number of "subranges" (radio, microwave, visible light, UV, X-ray) with the CCD of "electromagnetic-wavelength".  Between any pair of adjacent ranges, there is a quantitative "threshold" where what happens on one side of the "threshold" doesn't happen on the other.  For example, ordinary violet light doesn't damage my eyes (ionization).  But UVA and UVB do.

Why this interests me

It has occurred to me that this idea of quantitative "threshold" could be applied to the various "subranges" within any Conceptual Common Denominator of scientific interest.  Protein folding comes to mind.  The idea of a "threshold" can spur pursuit of the subtle interaction giving rise to the dramatic transition from NOT to DOES. Proteins in situations "near" the quantitative "threshold" between folding and not-folding can be used to discover why protein folding occurs when it does.

QUESTION:

Does the discovery of a quantitative "threshold" imply the existence of parts subtler than what is perceived?

Link to comment
Share on other sites

Is this any different than a borderline concept as Rand defined it? In a sense, there are infinite ways to divide up the world we perceive. I don't think Rand in particular ever argued for some fundamentally irreducible object (distinct from an entity, which is a fundamental starting point for grasping the world). By nature of a "borderline" existing at all, it just implies that a finer-grained analysis is possible to further distinguish concepts based on conceptual need. If you develop a need to find out what's at the border between microwaves and visible light, then any subtler parts are a matter of knowing what phenomena you want to comprehend. If you seek the exact threshold without some motivating phenomena, then you're arbitrarily drawing new lines.

Link to comment
Share on other sites

Louie said:

 

Quote

Is this any different than a borderline concept as Rand defined it?

 

Yes, your analysis of "borders" is a mistaken notion of what Ms. Rand's view of objectivity is. Your borders are actually arbitrary. Vik's points are ontologically objective and your view is actually epistemically subjective. The quantitative relationships Vik mentions are "measurements".....

Louie said:

Quote

I don't think Rand in particular ever argued for some fundamentally irreducible object (distinct from an entity, which is a fundamental starting point for grasping the world).

Of course she didn't.... She new that object and entity are synonyms. She did, however, argue for an entity based causation very clearly.

Edit: The ontological primacy of entities in Oism is the objective basis for the epistemic starting point of first level concepts... (which are  all entities)

 

Edited by Plasmatic
Link to comment
Share on other sites

2 hours ago, Plasmatic said:

Yes, your analysis of "borders" is a mistaken notion of what Ms. Rand's view of objectivity is. Your borders are actually arbitrary.

Okay, then explain how so. You have a tendency to say a lot, but not communicate it clearly. It looked to me that Vik was asking about a threshold by which to measure such that anything past some point of measurement will lack a certain attribute at all. Absolute zero is an example, and Kelvin is used to measure that. It serves a particular cognitive function, and also important is that it's a measurement of an object itself. I was not saying the border is whatever you'd like it to be.

I think your claim of ontological primacy of entities is coherent, but I was literally saying entities are an epistemic starting point. "Ontological primacy of entities" is vague though. If all objects are entities, electrons are entities, so then electrons are epistemic starting points? Hardly! Unless electrons aren't objects.

Note: for purposes of this thread, please just know by "entity" I'm trying to use a word to distinguish what people perceive without aid. Nothing else implied.

Edited by Eiuol
Link to comment
Share on other sites

20 hours ago, Eiuol said:

It looked to me that Vik was asking about a threshold by which to measure such that anything past some point of measurement will lack a certain attribute at all. Absolute zero is an example, and Kelvin is used to measure that. It serves a particular cognitive function, and also important is that it's a measurement of an object itself. I was not saying the border is whatever you'd like it to be.

To illustrate how to deal with "Absolute Zero", I will have to do some hierarchical reduction.

Part of the antecedent knowledge for understanding the Kelvin scale includes all knowledge antecedent to the Ideal Gas Law.  (In this context, I'm using "antecedent knowledge" to refer to that knowledge which is less abstract, historically earlier, and without which the more advanced knowledge could not have been attained)

The Ideal Gas Law was formulated by applying various concepts about units within a certain "sub-range" of temperatures and pressures. (By "sub-range", I mean a range that is narrower than and within the range of the CCD)

Do we need new concepts for cases "close" to the theoretical Absolute Zero?  Scientists have implied "yes":

The concept of a "superfluid" (frictionless fluid) was  applied to helium below 2.17 K. 

The concept of "Bose-Einstein condensate" (single quantum state) was applied by JILA at the University of Colorado at Boulder in 1995 to some behaviour they observed which was uncharacteristic of ordinary solids.

Link to comment
Share on other sites

5 minutes ago, Vik said:

To illustrate how to deal with "Absolute Zero", I will have to do some hierarchical reduction.

Part of the antecedent knowledge for understanding the Kelvin scale includes all knowledge antecedent to the Ideal Gas Law.  (In this context, I'm using "antecedent knowledge" to refer to that knowledge which is less abstract, historically earlier, and without which the more advanced knowledge could not have been attained)

The Ideal Gas Law was formulated by applying various concepts about units within a certain "sub-range" of temperatures and pressures. (By "sub-range", I mean a range that is narrower than and within the range of the CCD)

Do we need new concepts for cases "close" to the theoretical Absolute Zero?  Scientists have implied "yes":

The concept of a "superfluid" (frictionless fluid) was  applied to helium below 2.17 K. 

The concept of "Bose-Einstein condensate" (single quantum state) was applied by JILA at the University of Colorado at Boulder in 1995 to some behaviour they observed which was uncharacteristic of ordinary solids.

I say "theoretical" Absolute Zero because it lies outside of the context of how it was defined.

Link to comment
Share on other sites

4 hours ago, Vik said:

The Ideal Gas Law was formulated by applying various concepts about units within a certain "sub-range" of temperatures and pressures. (By "sub-range", I mean a range that is narrower than and within the range of the CCD)

Do we need new concepts for cases "close" to the theoretical Absolute Zero?  Scientists have implied "yes":

The concept of a "superfluid" (frictionless fluid) was  applied to helium below 2.17 K. 

What do you mean by subtler parts then - do you mean a threshold would only make sense if a subrange exists near absolute zero, say?

Link to comment
Share on other sites

1 hour ago, Eiuol said:

What do you mean by subtler parts then - do you mean a threshold would only make sense if a subrange exists near absolute zero, say?

Ordinary liquid phase of water and ordinary gas phase of water are separated by a mere degree.  That's a dramatic qualitative difference for the price of a tiny quantitative difference.

If you plot that special temperature for every ordinary pressure, you will find a sharp boundary between liquid phase and gas phase.  That is a quantitative "threshold".

In order to explain how liquid can become gas, you'll have to find some characteristic (of the constituents) differing quantitatively between the two phases.

Question:

Does the discovery of a quantitative "threshold" imply the existence of parts subtler than what is perceived?

Towards an answer:

In order to determine that, we will have to know something about what it is to be made of parts subtler than entities and what that means for causal inference.

After all, we take great pains not to neglect this in our thinking:

Quote

An entity is that which you perceive and which can exist by itself. Characteristics, qualities, attributes, actions, relationships do not exist by themselves.

 

Link to comment
Share on other sites

It sounds like you are making the mistake of thinking that the relation of parts to wholes (mereology) is that parts are themselves categorically different. By that, I mean to say that all parts are themselves entities...

 

You appear to be interested in the scientific realism debate. All theoretical objects, those hypothetical imperceptibles you call subtle causes, are still entities. Don't make too much out of the use of "perceptible" in the quote. Oism does not hold that to be an entity X must be perceptible.

 

 

Edited by Plasmatic
Link to comment
Share on other sites

1 hour ago, Plasmatic said:

Don't make too much out of the use of "perceptible" in the quote. Oism does not hold that to be an entity X must be perceptible.

Well, to be precise, Rand said entities in one sense are perceptual in scale. Another sense is when object and entity are synonyms. I mentioned it elsewhere before probably. Vik is using it in the first sense, as am I. I'm thinking on Vik's post still, I don't see why a quantitative threshold implies anything more subtle, unless there are phenomena near a threshold which cannot be explained by existing concepts or by behavior of existents you're aware of. Then again, it might not be due to a subtler constituent, it may be something unique about the existent itself or an interaction effect. 

Edited by Eiuol
Link to comment
Share on other sites

Introduction to Objectivist Epistemology 2nd edition pg. 264:

Quote

An entity is that which you perceive and which can exist by itself. Characteristics, qualities, attributes, actions, relationships do not exist by themselves.

Rand is absolutely right to ground concepts of entities in what is perceptible within the context in which this quote appears.  All other concepts are traceable to concepts of perceptible entities so she MUST advocate this definition here.

Historically, many false scientific theories have resulted from people trying to treat imperceptible constituents of matter as if they had the same properties as perceptible entities.  I have no desire for anyone to repeat such a blunder.

Furthermore, we know of things that are too different from perceptible entities for us to dare use the concept.  If you try to fire electrons one after another at a double slit, you get a wavelike pattern of arrival sites on the screen behind the double-slit.  If you shine a light on whatever has just passed through the slits, you get two dense rectangles of arrival sites on the screen. If you feel really perverse, you can condense valence electrons into a certain state by means of a magnetic field at low temperatures.  Then you have to say that you did NOT find whole-number charged things but instead found things with fractional electron charges.

The concept of electron is an abstraction from abstractions.  We have no right to act as if electrons are like the separable parts of a table.

As for scholarship:

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right, and you will need to convince me that it is more appropriate for philosophy of science than what she stated above.

Link to comment
Share on other sites

2 hours ago, Eiuol said:

I don't see why a quantitative threshold implies anything more subtle, unless there are phenomena near a threshold which cannot be explained by existing concepts or by behavior of existents you're aware of. Then again, it might not be due to a subtler constituent, it may be something unique about the existent itself or an interaction effect. 

If one side of the quantitative "threshold" cannot be explained by what is currently known, must there be some sort of activity responsible, regardless of whether or not there are subtler constituents than those observed?  What does it take to conclude that some activity unites both sides?

Link to comment
Share on other sites

louie said:

Quote

Well, to be precise, Rand said entities in one sense are perceptual in scale. Another sense is when object and entity are synonyms. I mentioned it elsewhere before probably.

And I have dealt with this claim extensively when you did so. Object and entity are synonyms in both the "primary sense " and in the "derivative sense" the only two sense Oism holds to. Your failed to give a differentia for you supposed category distinction.

Link to comment
Share on other sites

Vik said:

Quote

Rand is absolutely right to ground concepts of entities in what is perceptible within the context in which this quote appears.  All other concepts are traceable to concepts of perceptible entities so she MUST advocate this definition here.

All meaning is based on perception! There is NO context were we divorce semantics from perceptual reduction. 

 

Vik said:

Quote

Historically, many false scientific theories have resulted from people trying to treat imperceptible constituents of matter as if they had the same properties as perceptible entities.  I have no desire for anyone to repeat such a blunder

Then you will have to create a philosophy of science that is NOT justified by Objectivist epistemology.

 

ITOE said:

Quote

Prof. E: Suppose it were the case that worse comes to worst epistemologically, that at the outside limit of human cognition in the indefinite future, scientists will never get beyond a knowledge of the actions of the ultimate entities—because in effect human beings' means of cognition doesn't encompass any means of reaching the nature of the entities, except that it is a something which has identity and acts in a certain way. Would you regard that as having philosophic significance, were that to be the ultimate answer?

AR: No.

Prof. E: Would that prove that reality in itself is unknowable to us?

AR: No.

Prof. E: Or that all we can know ultimately is just action?

AR: No. Keep your terms defined. What are you talking about? You are talking about the constituents of what we, to begin with, perceive as entities. And to say we really can <ioe2_295> perceive only action, because on the sub-subatomic level we cannot grasp the nature of those entities, we can only grasp their actions, doesn't hold. All you are saying is: I can't go beyond a certain level of knowledge. That doesn't mean that all you grasp is action.

And you know what else is crucially important? When you talk about discovering the ultimate constituents of the universe, remember that in order to discover them, no matter by what calculations or by what machinery, you had to bring them to your perceptual level. You would have to say "this particle" is that which acts in such and such a way on subatomic particles, which act in such and such a way on atoms, which act in such and such a way on molecules, and all of that results in a material object such as this glass as distinguished from other material objects such as this ashtray. Unless you bring it back to the perceptual level, it's not knowledge. That is what has to be kept in mind always in speculating about ultimate causes, which have to be discovered by some, at present, unknown means. You still always have to bring it back to your sensory-perceptual level, otherwise it's not knowledge.

 

Vik said:

Quote

The concept of electron is an abstraction from abstractions.  We have no right to act as if electrons are like the separable parts of a table.

We have every philosophical right because "abstraction from abstraction" is a description of what human substantial entities DO and a concept of method is not a valid category for the science that discovers what KINDS of entities there are and how they act! (physics) Electrons are "theoretical entities" and that means we use concepts to explain hidden causes. WE do not then call these hidden causes "abstractions" ontologically.  A realist philosophy of science does not hold that electrons are abstract constructs but a discovery of an existential cause via induction.

Vik said:

Quote

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right, and you will need to convince me that it is more appropriate for philosophy of science than what she stated above

Objectivism holds to an "Entity based causation"

Philosophy tells us that "to be is to be an entity" (where "be" is referring to metaphysical primaries).. Physics tells us what kinds of entities there are and how they act.

 

The onus is on you to show me anywhere Mrs. Rand claims that there are actions, relationships, or processes that are not OF entities in the "primary" sense. You will also have to show me that you can use ANY concept meaningfully that is not derived from perception. Philosophers of science know this debate and have tried to find a semantics that can make "non material entity" meaningful. You cant do it with Oist semantic theory! You also cannot justify the current dualist view of light with an objectivist epistemology.

Philosophy of science follows from philosophy generally. There is no special pass for concepts in physics to use a different semantic criteria. We do not run experiments to determine what "entity" means! That is settled in Philosophy where all the subject matter is ubiquitously present in every moment of cognition..

Can you get from identity to causality without the concept "entity" in the primary sense? Nope. Unless your theoretical entities are not in fact causal agents..... A non-sequiter, I know.

Edited by Plasmatic
Link to comment
Share on other sites

Vik said:

 

Quote

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right [...]

 

ITOE said:

 

Quote

The first concepts man forms are concepts of entities—since entities are the only primary existents. (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships among entities.)  

[...]only entities are metaphysical primaries

What is unclear about these unequivocal statements? 

 

 

Edited by Plasmatic
Link to comment
Share on other sites

8 hours ago, Plasmatic said:

And I have dealt with this claim extensively when you did so. Object and entity are synonyms in both the "primary sense " and in the "derivative sense" the only two sense Oism holds to.

It literally says it here: http://aynrandlexicon.com/lexicon/entity.html

"An entity is perceptual in scale, in size. In other words it is a “this” which you can point to and grasp by human perception."

Anyway, mountains from molehills, I said I'm using the word entity in the above sense. If you know a better word for "something perceptible", let me know.

Edited by Eiuol
Link to comment
Share on other sites

8 hours ago, Plasmatic said:

louie said:

And I have dealt with this claim extensively when you did so. Object and entity are synonyms in both the "primary sense " and in the "derivative sense" the only two sense Oism holds to. Your failed to give a differentia for you supposed category distinction.

Rand explicitly stated that an entity is perceptible.

Link to comment
Share on other sites

Making mountains from mole hills would be taking the word "perceptible" and then treating everything else she said about entities as though it didn't matter. 

 

ITOE said:

 

Quote

Entities and Their Makeup  

What Is an Entity?  

Prof. K: I would like to ask you to clarify your use of the term “entity.” Specifically, on page 15, in speaking of perceptual entities, you state, “entities are the only primary existents’ Now, does this imply that you grant that there is a metaphysical status of entity apart from whether or not something is a perceptual entity?  For example, is it in principle possible for a perceptual entity to be composed of constituents which are metaphysically themselves also entities, such as a brick wall with the individual bricks also retaining their status as entities?  AR: Certainly.

[...]AR: A part of an entity is something that can be separated.  

Prof. E: And then becomes an entity, when it’s separated.

 AR:Yes.  

 

 

This is why its a bad idea to not consider everything an author said about a subject. 

The perceptible part is just to stress the ostensible nature of first level concepts.

Edited by Plasmatic
Link to comment
Share on other sites

7 hours ago, Plasmatic said:


ITOE said

At NO point in those quotes did Rand say that there are imperceptible entities.  And again, on page 246, Rand stated explicitly that an entity is what you can perceive. 

Quote
Quote

We have no right to act as if electrons are like the separable parts of a table.

We have every philosophical right

I told you several things about electrons that are NOT true of tables. You CANNOT apply everything you know of tables to "electrons".

Rand advocated showing how "electron" acts in such a manner on atoms which act in such a way on molecules and so on ultimately resulting in perceptible entities -- which is EXACTLY what I advocate.

 

Quote

"abstraction from abstraction" is a description of what human substantial entities DO and a concept of method is not a valid category for

I never said that an electron was a concept of method. 

Furthermore, not all abstractions from abstractions produce concepts of method.   Rand was crystal clear on how concepts of method work in Concepts of Consciousness.

I said that we cannot blindly attribute to electrons what we attribute to perceptible entities because they are on different levels of abstraction. 

Quote

the science that discovers what KINDS of entities there are and how they act

If you want to re-define the concept of physics, you're going to have to show me how this is a characteristic, let alone the fundamental one.

Quote

Electrons are "theoretical entities" and that means we use concepts to explain hidden causes.

Is this your definition of "theoretical entities"?

Quote

A realist philosophy of science does not hold that electrons are abstract constructs but a discovery of an existential cause via induction.

I'm not going to bother debating whether Objectivism implies a realist philosophy of science.  It seems like there are as many versions of realism as there are realists and anti-realists.

But I'm happy to name some contentions which might make discussion more productive.

I hold that the concept of "electron" has referents in reality.

I hold that we can discover an aspect of what it is to be an effect under investigation.

I hold that the concept of "electron" can be used to identify an aspect of a perceptible change under investigation.

I hold that conceptual identification involves a process of measurement-inclusion.

I hold that the concept of "electron" can be used to explain macro-scale change by identifying an aspect of the macro-scale change through a process of measurement-inclusion.

Quote
Quote

 

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right, and you will need to convince me that it is more appropriate for philosophy of science than what she stated above

Objectivism holds to an "Entity based causation"

Of course.

Quote

Philosophy tells us that "to be is to be an entity" (where "be" is referring to metaphysical primaries).

This needs clarification and support.

Quote

Physics tells us what kinds of entities there are and how they act.

You need to concretize this.

Quote

The onus is on you to show me anywhere Mrs. Rand claims that there are actions, relationships, or processes that are not OF entities in the "primary" sense.

I noticed you didn't quote the essential phrase "perceptible or not".

I'm going to put it back:

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right, and you will need to convince me that it is more appropriate for philosophy of science than what she stated above

Quote

You will also have to show me that you can use ANY concept meaningfully that is not derived from perception.

Why?  Every valid concept is derived meaningfully from perception.  I have no desire to use invalid concepts.

Quote

 

Philosophers of science know this debate and have tried to find a semantics that can make "non material entity" meaningful. You cant do it with Oist semantic theory!

Do you think it's necessary to talk about a non-material entity?

I have yet to see why we would need such a concept.

Quote

You also cannot justify the current dualist view of light with an objectivist epistemology.

Are you trying to bring up wave-particle duality? 

Quote

We do not run experiments to determine what "entity" means!

I never said that we do.

I have repeatedly referred to Rand's definition:

Quote

An entity is that which you perceive and which can exist by itself. Characteristics, qualities, attributes, actions, relationships do not exist by themselves.

What I said was that we shouldn't be in a hurry to call every imperceptible existent an entity.

An existent is something that exists, be it a thing, an attribute, or an action.

Quote

Length does exist in reality, only it doesn’t exist by itself. It is not separable from an entity, but it certainly exists in reality. If it didn’t, what would we be doing with our concepts of attributes? They would be pure fantasy then. The only thing that is epistemological and not metaphysical in the concept of “length” is the act of mental separation, of considering this attribute separately as if it were a separate thing.

How would you project a physical object which had no length? You couldn’t. And therefore if to say it is epistemological rather than metaphysical is to say it exists only in relation to your grasp of it, or it requires your grasp of it in order to acquire existence—it doesn’t. Surely, if anything is metaphysical, attributes are.

I emphasize: Attributes DO exist in reality.

Quote

Can you get from identity to causality without the concept "entity" in the primary sense?

Can you demonstrate that some concept we form about something imperceptible implies an imperceptible entity with all the properties that perceptible ones do?

Because that's what under discussion.  NOT causality as the law of identity applied to action.

Link to comment
Share on other sites

1 hour ago, Plasmatic said:
1 hour ago, Plasmatic said:

Making mountains from mole hills would be taking the word "perceptible" and then treating everything else she said about entities as though it didn't matter. 

 

ITOE said

 

This is why its a bad idea to not consider everything an author said about a subject. 

The perceptible part is just to stress the ostensible nature of first level concepts.

 

Bricks are perceptible.  They are NOT imperceptible.

What you quoted says nothing about whether "entity" can be imperceptible.

Quote

If you think Rand advocated using "entity" to mean ANY "primary" physical existent, perceptible or not, you will need to show me the exact context in which you think she used the term that way, you will need to convince me that your interpretation is right, and you will need to convince me that it is more appropriate for philosophy of science than what she stated above.

 

Link to comment
Share on other sites

On 12/24/2015 at 8:59 PM, Eiuol said:

What do you mean by subtler parts then - do you mean a threshold would only make sense if a subrange exists near absolute zero, say?

http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146

This sort of thing is why we shouldn't try to apply an equation outside of its conceptual context.  (Kelvin scale was established in part by the Ideal Gas Law, which was formulated on the basis of knowledge of matter under MUCH warmer conditions)

Whatever CCD unites what's "above" and "below" the theoretical "Absolute Zero", we need to form concepts appropriate to THAT sub-range of temperatures. 

I would like to see more people trying to figure out what happens near the theoretical "Absolute Zero".

Link to comment
Share on other sites

Only time for this:

Vic said:

At NO point in those quotes did Rand say that there are imperceptible entities.  And again, on page 246, Rand stated explicitly that an entity is what you can perceive.

Seriously? Yes it does!

 

Now, does this imply that you grant that there is a metaphysical status of entity apart from whether or not something is a perceptual entity?

to which she said "certainly"

Bricks are perceptible but the question is about the imperceptible constituents being granted the metaphysical status of entities. 

Link to comment
Share on other sites

 

12 hours ago, Plasmatic said:

Electrons are "theoretical entities" and that means we use concepts to explain hidden causes. WE do not then call these hidden causes "abstractions" ontologically.  A realist philosophy of science does not hold that electrons are abstract constructs but a discovery of an existential cause via induction.

This sounds very odd. I know what you mean by entity, to start off with. But why are electrons theoretical, are you suggesting electrons are not physical things...? I'm trying to see where a notable philosophical dispute is, because I find this more important of a bone to pick. 

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...